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Coarse-grained V representability.

Paul E Lammert1

  • 1Department of Physics, 104B Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA. lammert@phys.psu.edu

The Journal of Chemical Physics
|September 1, 2006
PubMed
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This study simplifies density functional theory by proving that coarse-grained electron densities are always representable by a unique external potential. This advances understanding of ground state densities for interacting electron systems.

Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Theoretical Chemistry

Background:

  • Density functional theory (DFT) relies on determining ground state densities.
  • The ensemble V-representability problem is a key unsolved challenge in DFT foundations.
  • Existing methods struggle with the complexity of interacting electron systems.

Purpose of the Study:

  • To address the ensemble V-representability problem in DFT.
  • To investigate a tractable, coarse-grained version of the problem.
  • To advance the theoretical understanding of ground state densities.

Main Methods:

  • Coarse-graining electron densities by averaging over spatial partitions.
  • Proving ensemble V-representability for strictly positive coarse-grained densities.

Related Experiment Videos

  • Demonstrating Gâteaux differentiability of the coarse-grained Lieb functional.

    • Main Results:

    • Every strictly positive coarse-grained density is proven to be ensemble V-representable.
    • A unique external potential, constant on partition cells, is shown to yield the prescribed coarse-grained density.
    • The coarse-grained Lieb functional is Gâteaux differentiable for confined systems.

    Conclusions:

    • The coarse-grained ensemble V-representability problem is thoroughly tractable.
    • This work provides a significant step towards solving fundamental DFT challenges.
    • Results are applicable to both closed and open quantum systems.